Abstract

Numerical solutions to the nonlinear coupled-wave equations of a
counterpropagating quasi-phase-matched device are analyzed by numerical
methods for both second-harmonic generation and cascaded
processes. Normalized derivations for second-harmonic generation
efficiency are also presented. The nonlinear phase shifts acquired
in this device by cascaded second-order processes are promising in
all-optical-switching applications. Specifically, a π/2 phase
shift is shown to be achievable with 42 times less input intensity than
the standard Type I configuration and 100% throughput. The effects
of metallic mirrors are also presented. Careful use of the phase
mismatch is shown to compensate for nonideal mirrors. Finally,
conservation of power in this configuration is briefly
investigated.

Figures (12)

Wave-vector matching diagrams for (a) FQPM, (b)
BQPM, (c) CQPM. There are two simultaneously phase-matchable
processes for cases (a) and (b), whereas there are six for case
(c). The FF and SH wave vectors are represented by thin black
and thin gray arrows, respectively. The grating wave vector
K = 2π/Λ is represented by a thick black
arrow. A dashed arrow represents the conjugate of the fundamental
wave.

Total intensity in the +ρ direction (black curve)
and -ρ direction (gray curve) for (a)
Γ2I0 = 0.2 and (b)
Γ2I0 = 3. The reflectivities
are taken to be rω = r2ω =
0.9. The offset is equal to the leakage at the mirror
Ileak.

Fundamental nonlinear phase shift (in units of π)
as a function of normalized input intensity
Γ2I0 and phase mismatch Δκ
(in units of π) for the CQPM device under study with
rω = r2ω = 1. The dashed
line represents the NLPS solutions found by a different numerical
method (i.e., the relaxation method).

Fundamental throughput as a function of normalized input
intensity Γ2I0 and phase mismatch
Δκ (in units of π) for the CQPM device under study with
rω = r2ω = 1. The viewpoint
in this figure is different from that of Fig. 6 to improve
legibility. The dashed line represents the throughput solutions
found by a different numerical method (i.e., the relaxation
method).